Find the general solution of the following first order linear ODEs: 1 (a) y' + ½/y = 3 cos(2t), t > 0 (b) ty' - y = t²et, t> 0 Find the particular solution of the following equations and initial conditions: (c) y' (t) - 2y(t) = (t + 2)², y(1) = 18 (d) y' - 3y = 3t+ 2e², y(0) = yo

Q: (b) у" — 2у + у 3 еt sin(z)

A:

Q: Verify that y(t)=C_(1)sin5t+C_(2)cos5t is a solution of y''(t)+25y(t)=0

A:

Q: Problem 1: Given f(x) = 1 + x² + cos(x) that is defined over 10,41 with a step (h)-1. Solve points…

A:

Q: 9y" + 25y = 0; y(37/10) = 0, y'(3x/10) = 3. %3D O a. y3-cos(음) O b. y = c cos(x) + cz sin() Oc…

A:

Q: Find Solution of Homogeneous linear ODE s (D°, 60 +131 Jy

A:

Q: Let 2² + y? = 1 and y(0) = 1 Then y'(0)= none of the listed here 1 -1

A:

Q: x A(x) = † (3-1²) dt 0

A:

Q: 3. Solve y' + cos(r)y = 2 cos z subject to the initial condition that y() = 2.

A:

Q: Suppose in an autocatalytic chemical reaction, compound A reacts to form compound B. Next, suppose…

A: Given that an autocatalytic chemical reaction, compound A reacts to form compound B. The initial…

Q: Solve the following nonhomogeneous ODES. (a) y" = -4y + e2#; (b) y" – 4y + 3y = e²; (C) y" = y+ e²…

A: Given that  The following differential equation  To find the general solutions

Q: The general solution of the 1st-order ODE, y' x² = Select one: a. y(x) = 2xx C+x b. y(x) = 2x -2² Cx…

A:

Q: Solve the first-order linear ODE t(t + 1)x' + tx = 6.

A:

Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

A: using the Euler's rule: yi+1=yi+hf(xi,yi) we will find the solution of given ODE we have…

Q: Solve y" + 2y + 2y = e cos(x) with y(0) = y'(0) = 1.

A:

Q: y' = xy³ (1 + x²)−¹/2, y (0) = 1

A: y'=xy3(1+x2)-12  dydx=xy3(1+x2)-12given  y(0)=1∫xndx=xn+1n+1+c