Internal problem ID [12198]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 148.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-7 y^{\prime }+12 y=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-7*diff(y(x),x)+12*y(x)=x,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{4 x} c_{1} +\frac {x}{12}+\frac {7}{144} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 30
DSolve[y''[x]-7*y'[x]+12*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x}{12}+c_1 e^{3 x}+c_2 e^{4 x}+\frac {7}{144} \]