8.7.26 problem 42

Internal problem ID [832]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 42
Date solved : Monday, January 27, 2025 at 03:09:26 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 35 y^{\prime \prime }-y^{\prime }-12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(35*diff(y(x),x$2)-diff(y(x),x)-12*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_2 \,{\mathrm e}^{\frac {41 x}{35}}+c_1 \right ) {\mathrm e}^{-\frac {4 x}{7}} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 26

DSolve[35*D[y[x],{x,2}]-D[y[x],x]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-4 x/7}+c_2 e^{3 x/5} \]