4. Find the unique solution y(x) to so that y(0) = 10 and y'(0) = 1. y" + 25y = 0, Hint: Start by finding a constant a so that cos(ax) and sin(ax) solve the equation.

Q: Solve (sin(x) cos(y)) dx + (cos(x) sin(y))dy = 0 if possible. If the equation is not exact, say so.…

A: First we check given differential equation is exact or not.  If given differential equation is exact…

Q: b. y - y'cosx = y² (1 - senx)cosx

A: Introduction: The Bernoulli's equation is an extension of linear first order differential equation…

Q: Find a general solution to the given equation. y""-7y"+11y'-5y = 9e + sinx Write a general solution…

A:

Q: Solve sin(x) +7 sin(x) cos(2x) = 0 for x E (0, 5). Give your answer in radians correct to 3 decimal…

A: The given equation is sin(x)+7sin(x) cos(2x)=0 and the range for x is (0, π/2).

Q: Solve for the particular solution of y' = 1/1 e 42 +3 sin 2x when x = 0 and y = 1

A: The differential equation is given by y' = 12e4x+3sin2x The initial condition is  y0 = 1 To…

Q: (e – y cos (x)) dx + (2xes (ey – y (xy) + 2y) dy x Cos cos = 0 3.

A: Exact differential equations

Q: h45. Solve for the general solution of y'= sinx + ycotx a. y = (x+ C)sinx b. y = Cxsinx c. y = (x +…

A:

Q: Solve D.E using bernouliis equation os(y)·y' + sin(y) =x

A:

Q: Verify if y = c, sin 3x + c2 cos 3x + 9x2 - 2 is a solution to y' +9y = 81a?. Show your solutions…

A:

Q: A. Eliminate the arbitrary constants of y = C₁ sin 2x + C₂ cos 2x + 3x². B. Prove that (y-2)(x - 1)…

A:

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y"-81y'…

A: Sol:- y'''-81y'=te-9t+10cos9tFirst , find the yh:-yh is the solution to the homogeneous ODE…

Q: Q: Solve y+8= Cos (x) ナ3sin(2x)

A: Given: y''+y=cos x+3 sin 2xCE: m2+1=0⇒m=±iCF: e(0)x( Acos x +B sin x)=Acos x +B sin x

Q: (cos y + y cos x) dx - (x siny - sinx) dy = 0

A:

Q: 9.) y(4) + 2y" +y = x² sinx

A:

Q: Find the root

A:

Q: 21. Solve the equation y' = (x²+ 7) / 9 (2x / 9) + c b. y = (x / 18) + c 22. Solve the equation y' =…

A:

Q: Find the first two positive solutions to 2 sin(3t) 1 t -

A: We have to find first two positive solutions to given equation.

Q: The given Riccati equation is y'- y²-yeatr + sin²x = 0 Also it is given that, the particular…

A: Solving Riccati equation when one particular solution is given. y=y1+1/u

Q: #1) Solve: 2 cos²x − cos x = 1 on [0,2π) —

A: Given ,  2cos^2(x) - cos(x) =1 on [0,2pi)   Substitute  u  for  cos⁡(x) .  2(u)2−(u)=1…

Q: f (t) =-e" sin (21 +7)

A:

Q: Q2: Find General Solution (YGS)to the equation (Yª-1) Y=COS(2x)

A: From the given information. The given differential equation is as follows.