BE Biomedical Engineering Semester 2 (FE First Year) - University of Mumbai Important Questions for Applied Mathematics 2

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Applied Mathematics 2
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Solve (2y^2-4x+5)dx=(y-2y^2-4xy)dy

Appears in 1 question paper
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Particular Integrals of Differential Equation

Solve (D^3+D^2+D+1)y=sin^2x

Appears in 1 question paper
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function

Solve the ODE (D-1)^2 (D^2+1)^2y=0

Appears in 1 question paper
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( x^a-1)/log x dx

Appears in 1 question paper
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function

Solve (1+x)^2(d^2y)/(dx^2)+(1+x)(dy)/(dx)+y=4cos(log(1+x))

Appears in 1 question paper
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 cycloid from one cusp to the next , where x=a(θ + sinθ) , y=a(1-cosθ)

Appears in 1 question paper
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function

Solve (D^2-3D+2) y= 2 e^x sin(x/2)

Appears in 1 question paper
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

Appears in 1 question paper
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

Appears in 1 question paper
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 .

Appears in 1 question paper
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

Appears in 1 question paper
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function

Solve by method of variation of parameters :(D^2-6D+9)y=e^(3x)/x^2

Appears in 1 question paper
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Method of Variation of Parameters

Solve (D^2-7D-6)y=(1+x^2)e^(2x)

Appears in 1 question paper
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.

Appears in 1 question paper
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function

Solve by variation of parameters ((d^2y)/dx^2+1)y=1/(1+sin x)

Appears in 1 question paper
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.

Appears in 1 question paper
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function

Using beta functions evaluate int_0^(pi/6)  cos^6 3θ.sinθ dθ

Appears in 1 question paper
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Particular Integrals of Differential Equation

Evaluate int_0^(a/sqrt2) int_y^(sqrt(a2-y^2)) log (x^2+y^2) "dxdy by changing to polar Coordinates".

Appears in 1 question paper
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 yzdzdydzover the volume bounded by planes x=0, y=0, z=0 and x/a+y/b+z/c=1

Appears in 1 question paper
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

Appears in 1 question paper
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
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