69.1.87 problem 132

Internal problem ID [14240]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 132
Date solved : Tuesday, January 28, 2025 at 06:23:06 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 20

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

\[ y(x)\to e^{3 x} \left (c_2 e^x+c_1\right ) \]