# BE Construction 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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Evaluate int_0^1 int_0^(x2) y/(ex) dy  dx

Appears in 2 question papers
Chapter:  Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function

Solve (D^2+2)y=e^xcosx+x^2e^(3x)

Appears in 2 question papers
Chapter:  Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function

Evaluate int_0^oo5^(-4x^2)dx

Appears in 1 question paper
Chapter:  Differential Equations of First Order and First Degree
Concept: Exact Differential Equations

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

Appears in 1 question paper
Chapter:  Differential Equations of First Order and First Degree
Concept: Exact Differential Equations

Solve  xy(1+xy^2)(dy)/(dx)=1

Appears in 1 question paper
Chapter:  Differential Equations of First Order and First Degree
Concept: Linear Differential Equations

Solve (y-xy^2)dx-(x+x^2y)dy=0

Appears in 1 question paper
Chapter:  Differential Equations of First Order and First Degree
Concept: Equations Reducible to Exact Form by Using Integrating Factors

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

Appears in 1 question paper
Chapter:  Differential Equations of First Order and First Degree
Concept: Exact Differential Equations

Solve ydx+x(1-3x^2y^2)dy=0

Appears in 1 question paper
Chapter:  Differential Equations of First Order and First Degree
Concept: Equations Reducible to Exact Form by Using Integrating Factors

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.

Appears in 1 question paper
Chapter:  Differential Equations of First Order and First Degree
Concept: Exact Differential Equations

Solve x^2 (d^2y)/dx^2+3x dy/dx+3y =(log x.cos (log x))/x

Appears in 1 question paper
Chapter:  Differential Equations of First Order and First Degree
Concept: Equations Reducible to Exact Form by Using Integrating Factors

Evaluate int_0^1 x^5 sin ^-1 x dxand find the value of β (9/2,1/2)

Appears in 1 question paper
Chapter:  Differential Equations of First Order and First Degree
Concept: Exact Differential Equations

Evaluate int_0^6 dx/(1+3x)by using 1} Trapezoidal 2} Simpsons (1/3) rd. and 3} Simpsons (3/8) Th rule.

Appears in 1 question paper
Chapter:  Differential Equations of First Order and First Degree
Concept: Simple Application of Differential Equation of First Order and First Degree to Electrical and Mechanical Engineering Problem

Evaluate (d^4y)/(dx^4)+2(d^2y)/(dx^2)+y=0

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

Show that int_0^1(x^a-1)/logx dx=log(a+1)

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

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

Appears in 1 question paper
Chapter:  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.

Appears in 1 question paper
Chapter:  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 parameter method (d^2y)/(dx^2)+3(dy)/(dx)+2y=e^(e^x).

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

Solve (D^3+1)^2y=0

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

Given int_0^x 1/(x^2+a^2) dx=1/atan^(-1)(x/a)using DUIS find the value of int_0^x 1/(x^2+a^2)

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

Evaluate int_0^∞ 3^(-4x^2) dx

Appears in 1 question paper
Chapter:  Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Concept: Legendre’S Differential Equation
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