75.15.2 problem 433

Internal problem ID [16953]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 433
Date solved : Tuesday, January 28, 2025 at 09:43:38 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime }-2 y^{\prime }-8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(3*diff(y(x),x$2)-2*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_{1} {\mathrm e}^{\frac {10 x}{3}}+c_{2} \right ) {\mathrm e}^{-\frac {4 x}{3}} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 24

DSolve[3*D[y[x],{x,2}]-2*D[y[x],x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-4 x/3}+c_2 e^{2 x} \]