69.1.128 problem 187

Internal problem ID [14281]
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
Date solved : Tuesday, January 28, 2025 at 06:25:34 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y&={\mathrm e}^{2 x} \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)-4*y(x)=exp(2*x)*sin(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (20 c_{2} -2 \cos \left (2 x \right )-\sin \left (2 x \right )\right ) {\mathrm e}^{2 x}}{20}+c_{1} {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 66

DSolve[D[y[x],{x,2}]-4*y[x]==Exp[2*x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (e^{4 x} \int _1^x\frac {1}{4} \sin (2 K[1])dK[1]+\int _1^x-\frac {1}{4} e^{4 K[2]} \sin (2 K[2])dK[2]+c_1 e^{4 x}+c_2\right ) \]