I only need help with part f.

4. a) Find the general solutions of the following differential equations. Express the general solution in y = f(x) whenever possible. dy x² = dx__y(1+x²) b) do dt =k(Q-70), k is any constant > 0

Find the nontrivial solution of each of the above equations.

Solve the following D.E: 9. e²y dx+2(xe²y - y)dy = 0 10. dy + x sin 2y = xcos²y dx 11. y" - 6y' + 9y= e³x = 12. y" y' 5ex - sin(2x) 13. y" - y' - 2y = 4x³

Solve with work please

Show that y₁=e* cos(2x) and y2 = e* sin(2x) are two linearly independent solutions of d'y dy +2- + 5y = 0 dx dx²

The solution of d²y dx2 dy 5- dx can be written as - 14y = 0 y(x) = Ae¹1x + Be^2x where >₁ > X2. Find A and B such that y(0) = -11, y'(0) = -6.

Find the general solution of y"+25y=sec(5x)