Solve `(D^2-3D+2) y= 2 e^x sin(x/2)`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Using D.U.I.S prove that `int_0^∞ e^-(x^+a^2/x^2) dx=sqrtpi/2 e^(-2a), a> 0`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Change the order of integration and evaluate `int_0^1 int_x^sqrt(2-x^2 x dx dy)/sqrt(x^2+y^2)`
[8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Concept: Differentiation Under Integral Sign with Constant Limits of Integration
Show that `int_0^asqrt(x^3/(a^3-x^3))dx=a(sqrtxgamma(5/6))/(gamma(1/3))`
[8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Concept: Differentiation Under Integral Sign with Constant Limits of Integration
Solve `(D^2+2)y=e^xcosx+x^2e^(3x)`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Evaluate `int_0^1int_0^( 1-x)1int_0^( 1-x-y) 1/(x+y+z+1)^3 dx dy dz`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Find the mass of the lemniscate 𝒓𝟐=𝒂𝟐𝒄𝒐𝒔 𝟐𝜽 if the density at any point is Proportional to the square of the distance from the pole .
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Solve` x^2 (d^3y)/dx^3+3x (d^2y)/dx^2+dy/dx+y/x=4log x`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Prove that for an astroid ` x^(2/3) +y2/3= a^(2/3)` the line 𝜽=𝝅/𝟔 Divide the arc in the first quadrant in a ratio 1:3.
[5] Differential Equations of First Order and First Degree
Chapter: [5] Differential Equations of First Order and First Degree
Concept: Exact Differential Equations
Solve `(D^2-7D-6)y=(1+x^2)e^(2x)`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Apply Rungee Kutta method of fourth order to find an approximate Value of y when x=0.4 given that `dy/dx=(y-x)/(y+x),y=1` 𝒚=𝟏 𝒘𝒉𝒆𝒏 𝒙=𝟎 Taking h=0.2.
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Use Taylor series method to find a solution of `dy/dx=xy+1,y(0)=0` X=0.2 taking h=0.1 correct upto 4 decimal places.
[7] Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function
Chapter: [7] Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function
Concept: Taylor’S Series Method
Solve by variation of parameters` ((d^2y)/dx^2+1)y=1/(1+sin x)`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Compute the value of `int _0.2^1.4 (sin x - In x+e^x) ` Trapezoidal Rule (ii) Simpson’s (1/3)rd rule (iii) Simpson’s (3/8)th rule by dividing Into six subintervals.
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Evaluate `int_0^(a/sqrt2) int_y^(sqrt(a2-y^2)) log (x^2+y^2) "dxdy by changing to polar Coordinates".`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Evaluate `int int int x^2` `yzdzdydz`over the volume bounded by planes x=0, y=0, z=0 and `x/a+y/b+z/c=1`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Evaluate `int_0^inftye^(x^3)/sqrtx dx`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Find the length of the curve `x=y^3/3+1/(4y)` from `y=1 to y=2`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Evaluate `int_0^1 int_(x^2)^x xy(x+y)dydx.`
[6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
