ODE
\[ \left (a^2+b^2\right )^2 y(x)-4 a b y'(x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.154331 (sec), leaf count = 62
\[\left \{\left \{y(x)\to e^{2 a b x-x \sqrt {-\left (a^2-b^2\right )^2}} \left (c_2 e^{2 x \sqrt {-\left (a^2-b^2\right )^2}}+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.042 (sec), leaf count = 45
\[[y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{2 a b x} \sin \left (\left (-a^{2}+b^{2}\right ) x \right )+\textit {\_C2} \,{\mathrm e}^{2 a b x} \cos \left (\left (-a^{2}+b^{2}\right ) x \right )]\] Mathematica raw input
DSolve[(a^2 + b^2)^2*y[x] - 4*a*b*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(2*a*b*x - Sqrt[-(a^2 - b^2)^2]*x)*(C[1] + E^(2*Sqrt[-(a^2 - b^2)^2]*x)*C[2])}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-4*a*b*diff(y(x),x)+(a^2+b^2)^2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(2*a*b*x)*sin((-a^2+b^2)*x)+_C2*exp(2*a*b*x)*cos((-a^2+b^2)*x)]