Solve `(4x+3y-4)dx+(3x-7y-3)dy=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: undefined >> undefined
Solve `dy/dx=1+xy` with initial condition `x_0=0,y_0=0.2` By Taylors series method. Find the approximate value of y for x= 0.4(step size = 0.4).
[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: undefined >> undefined
Solve `(d^2y)/dx^2-16y=x^2 e^(3x)+e^(2x)-cos3x+2^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: undefined >> undefined
Show that `int_0^pi log(1+acos x)/cos x dx=pi sin^-1 a 0 ≤ a ≤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: undefined >> undefined
Evaluate `int int int (x+y+z)` `dxdydz ` over the tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + y + z = 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: undefined >> undefined
Find the mass of lamina bounded by the curves 𝒚 = 𝒙𝟐 − 𝟑𝒙 and 𝒚 = 𝟐𝒙 if the density of the lamina at any point is given by `24/25 xy`
[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: undefined >> undefined
Evaluate `int_0^1 x^5 sin ^-1 x dx`and find the value of β `(9/2,1/2)`
[5] Differential Equations of First Order and First Degree
Chapter: [5] Differential Equations of First Order and First Degree
Concept: undefined >> undefined
In a circuit containing inductance L, resistance R, and voltage E, the current i is given by `L (di)/dt+Ri=E`.Find the current i at time t at t = 0 and i = 0 and L, R and E are constants.
[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: undefined >> undefined
Expand 2 𝒙3 + 7 𝒙2 + 𝒙 – 6 in power of (𝒙 – 2) by using Taylors Theorem.
[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: undefined >> undefined
Solve `dy/dx=x.y` with help of Euler’s method ,given that y(0)=1 and find y when x=0.3
(Take h=0.1)
[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: undefined >> undefined
Find the area inside the circle r=a sin𝜽 and outside the cardioide r=a(1+cos𝜽 )
[10] Triple Integration and Applications of Multiple Integrals
Chapter: [10] Triple Integration and Applications of Multiple Integrals
Concept: undefined >> undefined
Find the value of the integral `int_0^1 x^2/(1+x^3`𝒅𝒙 using Trapezoidal rule
[8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Concept: undefined >> undefined
Solve `(y-xy^2)dx-(x+x^2y)dy=0`
[5] Differential Equations of First Order and First Degree
Chapter: [5] Differential Equations of First Order and First Degree
Concept: undefined >> undefined
Evaluate `int int xy(x-1)dx dy` over the region bounded by 𝒙𝒚 = 𝟒,𝒚= 𝟎,𝒙 =𝟏 and 𝒙 = 𝟒
[10] Triple Integration and Applications of Multiple Integrals
Chapter: [10] Triple Integration and Applications of Multiple Integrals
Concept: undefined >> undefined
Solve` (2y^2-4x+5)dx=(y-2y^2-4xy)dy`
[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: undefined >> undefined
Evaluate `int int(2xy^5)/sqrt(x^2y^2-y^4+1)dxdy`, where R is triangle whose vertices are (0,0),(1,1),(0,1).
[10] Triple Integration and Applications of Multiple Integrals
Chapter: [10] Triple Integration and Applications of Multiple Integrals
Concept: undefined >> undefined
Use polar co ordinates to evaluate `int int (x^2+y^2)^2/(x^2y^2)` 𝒅𝒙 𝒅𝒚 over yhe area Common to circle `x^2+y^2=ax "and" x^2+y^2=by, a>b>0`
[10] Triple Integration and Applications of Multiple Integrals
Chapter: [10] Triple Integration and Applications of Multiple Integrals
Concept: undefined >> undefined
Solve `ydx+x(1-3x^2y^2)dy=0`
[5] Differential Equations of First Order and First Degree
Chapter: [5] Differential Equations of First Order and First Degree
Concept: undefined >> undefined
Compute the value of `int_0^(pi/2) sqrt(sinx+cosx) dx` usingTrapezoidal rule by dividing into six Subintervals.
[8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Concept: undefined >> undefined
Using beta functions evaluate `int_0^(pi/6) cos^6 3θ.sinθ dθ`
[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: undefined >> undefined
