29.2.11 problem 36

Internal problem ID [4644]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 36
Date solved : Monday, January 27, 2025 at 09:29:15 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

dsolve(diff(y(x),x) = 6*exp(2*x)-y(x)*tanh(x),y(x), singsol=all)
 

\[ y \left (x \right ) = 2 \tanh \left (x \right )+4 \cosh \left (x \right ) \sinh \left (x \right )+4 \cosh \left (x \right )^{2}+\operatorname {sech}\left (x \right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 42

DSolve[D[y[x],x]==6 Exp[2 x]- y[x] Tanh[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {6 e^{2 x}+2 e^{4 x}+c_1 \sqrt {e^{2 x}}}{e^{2 x}+1} \]