4. (а) Solve the IVP for y(t): y" + 4y = 3 8(t – n), y(0) = 0, y' (0) = 0 (b) 2n. Be sure to label your graph so that the period and amplitude of any oscillations are clearly identified. Graph the solution y(t) from part (a) versus t, for values of t between 0 and

Q: Find y as a function of x if y(1) = 8, y′(1) = 6. y = x²y" — 6xy' – 8y = 0,

A:

Q: 4. x. 5. y"+y sin² x.

A:

Q: 1. Find the function y(t) satisfying y' = ev-t(1+t?) sec y with y(0) = 0.

A: Claim: solution for with y(0)=0. Integrating both sides we get, Take u=e-y then du=-e-y  and…

Q: Use Picard's method to solve dx - Find y3(1)? -xy, y (0) = 1

A: Solution :-

Q: Function y = y(x) is given implicitly by x2y + y4 + sin(1 - y) = 4 + 2x (i) Find y′. (ii) Find y…

A: The given function is x2y+y4+sin(1-y)=4+2x. We have to find: y' y'' at P(-1,1) The product rule of…

Q: y" + 2y' = 4x – 5 cos(x).

A:

Q: 31+2 dy - of the function y= dt 7. Find +4 dy of the function y = 5 tan (6x)+ log, (36x² + dx 8.…

A:

Q: If a space shuttle's downward acceleration is given by y"(t) = –32 ft/s², find the osition function…

A:

Q: 3-(cos x)y' =yCv-1) sin x.

A:

Q: X(t) = b cos(wt) + V a² – b² sin²(wt)

A: We will use differentiation rules to solve this question.

Q: Identify f(x) to be used in variation of parameters to solve for y, e" y" + y' – 3y = x

A: To find f(x) write equation in form of y" + P y' +Q y = f(x).

Q: Find y as a function of t if y(0) = 8, y'(0) = 3. y = 64y" + 304y +361y = 0,

A:

Q: + √" y(7) cos(t — 7)dr, y(0) = 1. 2. Solve y' (t) = cos(t) +

A:

Q: The percentage of female high school graduates who enrolled in college is given in the table below.…

A: Let x represent time(in years) since 1970, and let y represent the corresponding percentage of…

Q: A particle moves along the x-axis, its position at time t seconds given by s(t) = et - 2t meters.…

A: The objective is to solve the above question.

Q: B. Find the first and second derivatives of the following: 1. m(x) = 2(x)(√x) 2. a(x) = √3x 3. [u(x)…

A:

Q: cy(1) = 4, y'′(1) = −2. y = x²y" +7xy +9y = xº,

A:

Q: (a) a²y + y sin r = xy. (b) y = x³y - 2y³. (c) y = e²-2y (d) y'= x² + y² xy

A:

Q: For y(t) solution of y'=-4y(1-y/4)+3 find the intervals where the function of t is increasing or…

A:

Q: Q3 Find dy/dx on the graph y sec x? + y? = cos2x at point (1, 2).

A: Derivative of implicit function

Q: II. Find dy/dx of the following functions: 1. y = cosh √√4x²+3 2. y= sec hx² x² +1 3. y=xcsche4x

A: See this solution in below

Q: Show that both R and R2 may be covered by countably many open balls.

A:

Q: Find the function y = f(x) whose graph passes through the point (5π/12,3.5)if dy/dx =cos(2x−π/3).

A:

Q: cos(t)y'-tsin(t) = y ; is this seperable or non-seperable?

A: It can be shows that it is not separable. See the next step

Q: Find the PS for (x²y" + 2xy' - 12y = 0 y(1) = 1 y'(1) = −1

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with  so here we have

Q: Solve the nonhomogeneous equation using the method of undetermined coefficients: y +4y=x-2 cos 2x,…

A: The solution is given as

Q: Find the derivative dv/dpsi of v(x) V()| V(vi) where V(y) = (1 - e-√2 and 16 V (vi) = (1 - e-√2…

A: Given v(ψ)=VψVψi           (1) where Vψ=1-e-16π3ψ2 and Vψi=1-e-16π3ψi2 Since ψi≠ψ and ψi is the…

Q: 6. Solve: y"(t) = te', y(0)=0, y'(0)=1

A: Given data y"(t)=tet  y(0)=0, y'(0)=1

Q: (31) Use Newton's Method to make the second approximation x2 to the solution of 2e" = ex. Take x1 =…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.