69.1.116 problem 167

Internal problem ID [14269]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 167
Date solved : Tuesday, January 28, 2025 at 06:25:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-7*diff(y(x),x)+6*y(x)=sin(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{6 x} c_{2} +{\mathrm e}^{x} c_{1} +\frac {7 \cos \left (x \right )}{74}+\frac {5 \sin \left (x \right )}{74} \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 66

DSolve[D[y[x],{x,2}]-7*D[y[x],x]+6*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (\int _1^x-\frac {1}{5} e^{-K[1]} \sin (K[1])dK[1]+e^{5 x} \int _1^x\frac {1}{5} e^{-6 K[2]} \sin (K[2])dK[2]+c_2 e^{5 x}+c_1\right ) \]