Internal problem ID [12213]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-7 y^{\prime }+6 y=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-7*diff(y(x),x)+6*y(x)=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{6 x}+c_{2} {\mathrm e}^{x}+\frac {7 \cos \left (x \right )}{74}+\frac {5 \sin \left (x \right )}{74} \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 32
DSolve[y''[x]-7*y'[x]+6*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {5 \sin (x)}{74}+\frac {7 \cos (x)}{74}+c_1 e^x+c_2 e^{6 x} \]