5. Consider the DE (y² with the initial condition y(0) = e (a) (b) cos(x)-3x²y-2x) dx +(2y sin(x) − x³ + ln y) dy = 0 Show all the work to show that this is an exact equation Use the technique discussed in class involving partial integration to solve the DE.

Q: 11. Let {(x, y) : x² + y² < 1} D = be the unit disc and f(x, y) = x² – 2x + y² + 2y + 1. Find the…

A:

Q: Now solve the ordinary differential equation (ODE) boundary value problem: v"(y) – X²v(y) = 8(y –…

A: We will use the Laplace transform to solve the given ODE.

Q: cos(x) * еУ + 9у %3D Зу8 — 5х + 10е =

A: The expression cos(x)×ey+9y=3y8-5x+10e. We have to find y' or dydx.

Q: Consider the differential equation dy dr − (y+10) (y+4)³ (y − 2) (y² + 2) Determine lim y(x) if y(0)…

A: We have to determine lim y(x) if y(0)=-8 as x -&gt;

Q: 2. Find all solutions: dt dy dx = 4x + y x + 4y' x > 0.

A:

Q: 2. Solve for y in the equation y = e* sin x + e* cos x – y +c 3. Solve for f e* sin x dx in the…

A: Given, (2) y = exsinx +excosx -y +c  We have to solve for y (3) ∫ex sinx dx = ex sinx + ex cosx -…

Q: SHOW WHETHER THE FOLLOWING DE IS EXACT OR NOT 1. (y^2 – 2x)dx + (2xy + 1)dy = 0 2. x[1 – sin(y)]dy =…

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

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: Find the general solution of the inhomogeneous second-order linear ODE 2( 24" - 5' 3u)= 2(10 sinx)

A:

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

A: The solution is given as