Solve each of the following boundary-value problems. (b) æ®g’’ = 1+ *; y(1)=y(1) = y"(1) = 0 (c) d²s/dt2+12t = 16 sin t; 8=2, ds/dt = -4 at t = 0

Q: Solve the following DE ty" + 2y' + ty = 0 y(0)=1

A: Given: The differential equation is ty''+2y'+ty=0 and the initial condition y0=1 To find the…

Q: 8. (t² + 3) cos(5t) dt

A:

Q: 9 ²+2y=2 cos²/ 2 di with y(0) - 3 dy (0) = -1 2 dt

A:

Q: Given a particle with the position function r(t) = t/ti+ (Int) j+ eʻk,

A: (a)    r(t)=tt i+lntj+etk Differentiate both sides with respect to t   ddt(r(t))=r'(t) =…

Q: 2(y + 1)e* dx + 2(ex - 2y)dy = 0

A:

Q: 4. Find f. (a) f'(x) = 1+3Va, f(4) = 25 (b) f"(0) = sin(0) +cos(0), f(0) = 3, f'(0) =

A:

Q: 1.11 Determine if the following equations are linear or nonlinear: a. y = 4 15x 3 b. y = 3x X c. y =…

A: We have to determine following equation is linear or not. Note:- These are multiple sub parts we can…

Q: Q.3 ) Solve the following D.Es: 1. 4d²y d¡ 2 +y =0. when t=0, y=1 and dt dy :-2. dt 2. xy =(1–x 2)y…

A: The solution to the given differential equations is explained below.

Q: Find the particular solution to the equation y'' + 6y' + 9y = e Yp(t) = - 3t arctant

A:

Q: Solve each of the following equations. 1.y( x² – y + 1) dx + x( 3x – 4y + 3) dy =o 2.Siny (x + sin…

A: Consider  the equation

Q: O XsinCyldx +(x^t)cos(y) dy=0

A: We have  xsinydx+x2+1cosydy = 0  x2+1cosydy=-xsinydx cosydysiny=-xdxx2+1

Q: 22. (e¹ + y) dx + (2 + x + ye³) dy = 0, y(0) = 1

A: Given ex+ydx+2+x+yeydy=0 and y0=1

Q: (5) Solve the IVP:dy - y = e* cos(2x), y(0) = 2 dx

A:

Q: Given I = = 16 sint +6 and y = 16 cos t +2 da (i) dt 16* cos(t) dy (ii) 16*sin(t) %3D dt dy (iii)…

A:

Q: y" + 4y = (t - 2) (t − 2) with y(0) = 0 and y'(0) = 1

A:

Q: Find solution of equation 2 o(x) = 2f cos(x-1t) ø(1)dir

A:

Q: 3. Find the position and velocity of the particle if its acceleration is a(t)=-cos(t)i – sin(t)j…

A:

Q: (a) Solve the equation, = 4e cos 2x subject to the boundary conditions that dxdy d?u du at y = 0, dx…

A:

Q: Use a substitution to find the implicit solution to the equation dy dt tan(t + y)

A: Given differential equation:To find:Solution of  using substitution method

Q: Integrate e* cos(x) dr COS

A: To evaluate: ∫02πexcosxdx To solve this we will use integration by parts

Q: 9. Obtain the general solution to the equation. (X² +36) dy + xy = 7x, y(0) = 2 dx

A: To obtain: The general solution to the equation X2+36dydX+Xy=7X, y0=2

Q: Calculus Question

A:

Q: Order | Degree Indepenc ependen Partial Linear Variable Variable y' = x +óy y" = 4y +y3 (d²y' \dx² +…

A: Note: Ordinary differential equation: An differential equation which involves dependent variable,…

Q: 20. Let h be the function defined by h(x) = [", sin²r dt. Which of the following is an equation for…

A:

Q: o(e) = La t -Va V1 + t²

A:

Q: II. Solve the general solution of the following:

A: The differential equation is                                       dydx=ysinx Separating the…

Q: 1) [ (2t–1)² dt 2 2 2) dx X 3) [ , x(x² + 1)° d.

A:

Q: 19. Calculate: -12e* (b) (25t – 8e') el-3 dt (a) dt (c) dx Hint for (c): Write e'-3 as e-³e'.

A: