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Question Bank Solutions for BE Automobile Engineering Semester 2 (FE First Year) - University of Mumbai - Applied Mathematics 2

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Applied Mathematics 2
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Evaluate `int_0^oo5^(-4x^2)dx`

[5] Differential Equations of First Order and First Degree
Chapter: [5] Differential Equations of First Order and First Degree
Concept: Exact Differential Equations

Evaluate `(d^4y)/(dx^4)+2(d^2y)/(dx^2)+y=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

Evaluate `int_0^1sqrt(sqrtx-x)dx`

[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 : `(1+log x.y)dx +(1+x/y)`dy=0

[5] Differential Equations of First Order and First Degree
Chapter: [5] Differential Equations of First Order and First Degree
Concept: Exact Differential Equations

Evaluate I = `int_0^1 int_0^(sqrt(1+x^2)) (dx.dy)/(1+x^2+y^2)`

[9] Double Integration
Chapter: [9] Double Integration
Concept: Double Integration‐Definition

Find the volume of the paraboloid `x^2+y^2=4z` cut off by the plane 𝒛=𝟒

[10] Triple Integration and Applications of Multiple Integrals
Chapter: [10] Triple Integration and Applications of Multiple Integrals
Concept: Triple Integration Definition and Evaluation

If 𝒚 satisfies the equation `(dy)/(dx)=x^2y-1` with `x_0=0, y_0=1` using Taylor’s Series Method find 𝒚 𝒂𝒕 𝒙= 𝟎.𝟏 (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: Taylor’S Series Method

Evaluate `int int int sqrt(1-x^2/a^2-y^2/b^2-x^2/c^2 )`dx dy dz over the ellipsoid `x^2/a^2+y^2/b^2+z^2/c^2=1.`

[10] Triple Integration and Applications of Multiple Integrals
Chapter: [10] Triple Integration and Applications of Multiple Integrals
Concept: Triple Integration Definition and Evaluation

Evaluate `(2x+1)^2(d^2y)/(dx^2)-2(2x+1)(dy)/(dx)-12y=6x`

[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

A resistance of 100 ohms and inductance of 0.5 henries are connected in series With a battery of 20 volts. Find the current at any instant if the relation between L,R,E is L `(di)/(dt)+Ri=E.`

[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 `(D^3+1)^2y=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

Solve the ODE `(y+1/3y^3+1/2x^2)dx+(x+xy^2)dy=0`

[5] Differential Equations of First Order and First Degree
Chapter: [5] Differential Equations of First Order and First Degree
Concept: Exact Differential Equations

Use Taylor’s series method to find a solution of `(dy)/(dx) =1+y^2, y(0)=0` At x = 0.1 taking h=0.1 correct upto 3 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 `(D^3+D^2+D+1)y=sin^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

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

Evaluate `int_0^1 int_0^(x2) y/(ex) dy  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 volume enclosed by the cylinder `y^2=x` and `y=x^2` Cut off by the planes z = 0, x+y+z=2.

[10] Triple Integration and Applications of Multiple Integrals
Chapter: [10] Triple Integration and Applications of Multiple Integrals
Concept: Triple Integration Definition and Evaluation

Evaluate `int_0^1( x^a-1)/log x 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

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

Find the length of cycloid from one cusp to the next , where `x=a(θ + sinθ) , y=a(1-cosθ)`

[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
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Question Bank Solutions for BE Automobile Engineering Semester 2 (FE First Year) University of Mumbai Applied Mathematics 2. You can further filter Question Bank Solutions by subjects and topics. Solutions for most of the questions for University of Mumbai can be found here on Shaalaa.com. You can use these solutions to prepare for your studies and ace in exams. Solving questions is a great way to practice and with Shaalaa.com, you can answer a question and then also check your answer with the solutions provided.
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