69.1.101 problem 148

Internal problem ID [14254]
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
Date solved : Tuesday, January 28, 2025 at 06:23:21 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)-7*diff(y(x),x)+12*y(x)=x,y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{4 x} c_{1} +\frac {x}{12}+\frac {7}{144} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]-7*D[y[x],x]+12*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x}{12}+c_1 e^{3 x}+c_2 e^{4 x}+\frac {7}{144} \]