69.1.90 problem 135

Internal problem ID [14243]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 135
Date solved : Tuesday, January 28, 2025 at 06:23:12 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+3*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {x \left (-3+\sqrt {17}\right )}{2}}+c_{2} {\mathrm e}^{-\frac {\left (3+\sqrt {17}\right ) x}{2}} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}]+3*D[y[x],x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\frac {1}{2} \left (3+\sqrt {17}\right ) x} \left (c_2 e^{\sqrt {17} x}+c_1\right ) \]