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 = 0.00661155 (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 = 0.023 (sec), leaf count = 44
\[ \left \{ y \left ( x \right ) =-{{\rm e}^{2\,abx}} \left ( \sin \left ( {a}^{2}x-{b}^{2}x \right ) {\it \_C1}-\cos \left ( {a}^{2}x-{b}^{2}x \right ) {\it \_C2} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = -exp(2*a*b*x)*(sin(a^2*x-b^2*x)*_C1-cos(a^2*x-b^2*x)*_C2)