Find the solution of the given initial value problem: y(t) = = y (4) + 2y""+y" + 8y' - 12y = 12 sin(t) + 40e-t; 48 94 5 4 y(0) = 0, y'(0) = y"(0) = 5, y" (0) " 5 5' =

Q: Find the solution of y" + 9y' = 162 sin(9t) + 1296 cos(9t) %3D with y(0) = 5 and y' (0) = 9. %3D y =

A:

Q: Given y(x) = c₁e²x + c₂e* + 2 sinx, find the values for ₁ and ₂ so that the conditions y(0) = 0 and…

A:

Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

A:

Q: 7. The velocity of an object traveling along a straight line is v(t) = cos(t) + 4t + 1 meters per…

A: Solved below

Q: Show that there is exactly one solution f E L'([0, 1]) of the equation f(x) = 7 + sin(x) %3D

A:

Q: Find the general solutions (implicit or explicit) to the following equations. (a) y' = e3x-2y + x²…

A: First order ordinary differential equation.

Q: What is the solution of the following equation: y(t) sin(t – t) dt = t Select one: a.…

A:

Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

A:

Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: 5. Solve the particular solution of (D2 + 1) y = sec (x) tan (x) using variation of parameters

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: s (oint 4x Casq 4x) dx

A:

Q: If dy/dx=sin(x)cos2(x)dx and y(pi/2)=0, whats the value of y(0)?

A: I am going to solve the given problem by integrating the given differential and by substituting the…

Q: 5. Find the solution(s), if any, of the following equations. (a) cos (2x) = 5 cos(x) + 2, where a E…

A: Given:- cos(2x) =5cos(x) +2 when x∈ [0, 2π] csc-1(-√(x2+1)) -tan-1(-√3) =cos-1(1)  To find:-…

Q: Solve the following Clairaut equation   y=xy'+(y')^2

A: Firstly we will differentiate this equation to get simpler differential equation

Q: Find all the solutions to sinh(z) = i/2

A: Solutions are:z=i(1+12k)6π​,k∈Zandz=i(5+12k)6π​,k∈ZExplanation:Step 1:Step 2: Step 3: Step 4:

Q: Find the general solution: 2y" + 3y' +y = 2e2 + x² + 3 sin(x).

A:

Q: Find the solution of y" + 4y = 160 sin(4t) + 224 cos(4t) with y(0) = 3 and y' (0) = 2. y =

A:

Q: the solution to the given equa y" + y' – 2y = cos(x) – 3 sin(: -

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: (i) By sketching the graphs of y = 4 sin x and y= e" on the same coordinate system, find the number…

A:

Q: If y(t) is the general solution for the equation: y' + y = sin(t), y(pi/2) = 0 Then, y(0) = ? a)…

A: Consider the differential equation  y'+y=sint,           yπ2 = 0

Q: Find the solution to the given equations: (a) y" + y' – 2y = cos(x) – 3 sin(2x), y(0) = 1, y'(0) = 2…

A:

Q: satisfied

A: We will solve the problem.

Q: 3. Which of the following gives if y=sin" (2x)? dx 2 (A) V1-4x 1 (B) V1- 4x 2 (C) V1-4x 1 (D) V1-4x…

A: To find the dy/dx

Q: Use undetermined coefficients to find the particular solution to y'' + y' – 30y = (1160t –…

A: The given problem is to find the particular solution for the given non homogeneous differential…