Use the method for solving Bernoulli equations to solve the following differential e + 7y = e*y¯? dx Ignoring lost solutions, if any, the general solution is y =. (Type an expression using x as the variable.)

Q: у" - 9y' %3D 27

A: The solution are next step

Q: Find the solution to the following differential equa tion: d²y dt2 dy +3- dt + 2y = e-t y(0) = 0,…

A:

Q: 3. xdy - ny dx = x"*1 dx %3D 4. 2x y' = y( y + 3x? ) 5. dy/dx +(y/x) = ( y/x )?

A:

Q: dy dx 2₁ y x = x + 2√/ X X

A:

Q: 8. y' = 1+3y tan x

A: Consider the equationy'+p(x) y=q(x)IF=e∫p(x) dxSolution is y(IF)=∫q(x).IF dx

Q: olve the d

A: Given,         dxdt=37.5-3.5x

Q: (a). 2t²u" + 3tu'- u = 0,t> 0

A: The given differential equation is,let us substitute t=ez so z=logt and hence

Q: cQl Solve the differetial equat'ron Sin (2x)+ 5 Sin(2x)+ 3 eos (20)

A: As per the question we are given a linear non-homogeneous second order ordinary differential…

Q: dy = -y + 2 with the initial value y(0) = -2 dx

A: Explanation of the answer is as follows

Q: Solve the homogenious differential equation Cy²+4y+4y=0; ylo)=1, y'(0) = 3 2 2 ⑤[ +² D² + 5 + D…

A: The homogeneous  differential equation is:The aim is to solve the homogeneous differential equation.

Q: y = Cje² + C2xe* + C3x²e* %D O y" + 3y" + 3y' + y = 0 y" – 3y" + 3y' + y = 0 %3D + 3y" + 3y' – y = 0…

A: Given data is: y=C1ex+C2xex+C3x2ex

Q: aur + 2xyury + y*uyy = 0

A: