The general solution to the differential equation y"+10y'+(e²x-7)y=0 1 y=f(x)(C₁ Ja (g(x)) + C₂ Ya (g(x))). Write this form of the general solution using the correct value for the constant a and the correct functions of x represented by f(x) and g(x). has the form y= a = f(x) = and g(x) = Hints: Try using a new independent variable z=ex and a new dependent variable w=e¹0x/2 y.

The solution of the differential equation x2y" - 2xy' + 6y = 0 (x > 0) is the function y(x) = C1 y1(x) + C2 y2(x). Find y1(x) and y2(x). Also, find the constants C1 and C2 if y(1) = - 1, y'(1) = 1.

Solve the differential equation y' – 2y = x²e3x

Form a differential equation by eliminating the arbitrary constant a and b from the equation y = ax² 2bx