(D² – y = Te 1 3D+ 2) 1+e-x

Q: Ex. Find the general solution to dy 1 -2.x dx X -

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Q: 8. (D2 – 10D + 34)y = -cos3x

A: Answer and explanation is given below

Q: Q6: Determine a particular solution of the equation d'y +4y 4x cos 2x dx Using D-operator method

A: The solution is given as

Q: If x=t² - 5t and y=1-61² , then dy at t =1 is dx Oa. 4 O b. -1 - 4 d. 4

A: We need to find parametric differentiation

Q: dy Зу +4 Find the general solution: %3D dx 2y + 3

A: Topic - differential Equationd By separating Variables method

Q: 1 В(т, п) ym-1(a – y)"-'dy. am+n-1

A:

Q: Solve D.E using Exact from first order 2.xy dx +(x² +3y²)dy

A: To solve the given differential equation.

Q: 2) Obtain the DE with respect to x of (x - h)² = 4(y-k).

A: Sol

Q: 2. (e2y – y cos xy)dx + (2xe2y - x cos xy + 2y)dy = 0

A: Exact differential equation

Q: Solve this DE in Non-Exact method: (x2+6y2)dx-4xydy=0 ; y(1)=1

A:

Q: dr - (x- 2) ey dy = 0

A: Given Differential equation is linear. We will solve it by finding integrating factor

Q: 10. (x2+y)+(x+ey)dydx=0

A: We have given the equation;

Q: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

A: The Leibnitz rule for differentiation under integral sign is,…

Q: The approximation of I = (x-3)e* dx by composite Trapezoidal rule with %3D n=4 is:

A:

Q: d²y dy y = e * is a solution of dx2 = 0 dx

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Q: Obtain the general solution. d²y e* 1. dx? dy 2 +y= dx x² +1

A:

Q: 4. (D² – 10D + 34)y = -cos3x

A: Using method of Linear Differential Equations with constant coefficients.

Q: n/3 SS ycos(xy)dydx= - π/ 3

A:

Q: d²y 2) Obtain a particular solution for d*y dx+ + + y = x³ + 2x +1 dx2

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Q: 4. S Sp(x² + y³)dxdy, wherein B = {(x, y) E R²; 0< x² + y² < 1}

A:

Q: -2dх 38. y-2dx dy er e2x + 1' УО) %3D 1

A:

Q: 1² + 3x + 4 If t = (r² – 1) what is dt/dx?

A: We have to find derivative

Q: Solve th D.E using Exact (6x² – y +3)dx+(3y – x – 2)dy

A:

Q: Solve the equation (4y + 2x – 5 dx + (6 y + 4x – 1 dy = 0 subject to the initial condition y(-1)= 2.…

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Q: d S[e-In(2t+1)]dr. find g(x) - dx A e-In(2x+1) 2 B (2x + 1)² (2x + 1)² (2x+1)² If g(x) = D

A: We have to find out the derivative

Q: Express æ = e-t, y = 2e2" in the form y = f(x) by eliminating the parameter y =

A:

Q: Q2 Find (d y/d x)& (dy/dx²) ex = 1/ cosxy

A: Given: eyx=1cos xy ⇒eyx(cos xy)=1 ----(1) Differentiate equation (1) w.r.t "x" ddxeyx(cos xy)=ddx(1)…

Q: d² dy +5 dy + 5y = e-t sint, where y(0) = 0 and y' (0) = 1.

A: Given: The equation is d2ydt2+5dydt+5y=e-tsint. The given initial condition is y0=0 and y'0=1. To…

Q: (c) Find the specific solution to d²y dx² when x = 0,= 0 and y = 1 +4 dy dx + 5y = 0

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Q: dy Given y x" In (2x), determine dx ax"- In (2x) + a-1 a.a"- In (2x) + 2.x O...n 1 None of these ax…

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Q: Solve D.E using Exact from first order (6x² - y+3)dx+(3y² – x- 2)dy

A:

Q: c3 Q3/ Evaluate , S(6x³ + 6y²) dx dy using Simpson's 1/3 rule in x-axis and Trapizodal rule in y…

A: Given ∫23∫466x3+6y2dxdy

Q: Solve for the general solution * (eУ — усos ху) dx + (2xe-У — х соs ху +2у) dy %3D0

A:

Q: In Prob. 1-38. Find dy/dx.

A: Given; y=e2x+3.

Q: Q11) The solution of (1 – y² )dx + (1+ x² )dy = 0 is: %3D

A: 1-y2dx+1+x2dy=0 On simplification, we get ⇒1-y2dx=-1+x2dy⇒dx1+x2=-dy1-y2

Q: 2. Solve the IVP 2x + y + 2xyy' = 0, with y(1) = –2. d (Hint: This ODE is neither first order…

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Q: dy Solve the initial – value problem: = y² given that f(0) = -1 dx %3D

A:

Q: Q3) (cos y – 2xy + dx – (x² + xsin y)dy = 0 x²+

A: Simplify the equations by grouping like terms and using the product rule of differentiation. Look…

Q: Solve the D.E. 3 2 y sin ex-³y ros²x de ²

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Q: 35. Find a value of the constant k so that kx²y dx dy = 1.

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Q: blö7 Q2: choose the correct answer If y = %3D t^2/(t^2+1) and t= v(2x+1) the dy/dx = %3D

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Q: dy 2. Find the general solution to the ODE dx 3x %3D x + 1

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Q: find d^2y/dx^2 implicitly in terms of y and x  2y^3=3x^4

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Q: If x = 5t +4 and y = 3t-7 , then find dy at t = 2. dx а. 1 O b. 2

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Q: 2. x3 – y3 = c³, find y" %3D d²x 3. x* = at?, find dt2

A: we need to find d2ydx2 from equation x3-y3=c3

Q: Solve: 3(1 + t?)(dy/dt) = 2ty(y³ - 1). %3D

A: Solve the integral 31+t2dydt=2tyy3-1. Use the separation of variable method. 1yy3-1y'…

Q: ) Solve the D.E xy(x²+ 1)dy- (y2 + 1)dx 0 %3D

A: