Internal problem ID [3300]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+y \tanh \left (x \right )=6 \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x) = 6*exp(2*x)-y(x)*tanh(x),y(x), singsol=all)
\[ y \left (x \right ) = 2 \tanh \left (x \right )+4 \sinh \left (x \right ) \cosh \left (x \right )+4 \cosh \left (x \right )^{2}+\operatorname {sech}\left (x \right ) c_{1} \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 33
DSolve[y'[x]==6 Exp[2 x]- y[x] Tanh[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x \left (6 e^x+2 e^{3 x}+c_1\right )}{e^{2 x}+1} \]