Internal problem ID [12225]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 187.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y=\sin \left (2 x \right ) {\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)-4*y(x)=exp(2*x)*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{-2 x}-\frac {{\mathrm e}^{2 x} \left (2 \cos \left (2 x \right )+\sin \left (2 x \right )\right )}{20} \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 42
DSolve[y''[x]-4*y[x]==Exp[2*x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{2 x}+c_2 e^{-2 x}-\frac {1}{20} e^{2 x} (\sin (2 x)+2 \cos (2 x)) \]