Internal problem ID [4770]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page
403
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+y \tanh \left (x \right )=2 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x)+y(x)*tanh(x)=2*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (x +c_{1} \right ) \operatorname {sech}\left (x \right )+\cosh \left (x \right )+\sinh \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 29
DSolve[y'[x]+y[x]*Tanh[x]==2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x \left (2 x+e^{2 x}+c_1\right )}{e^{2 x}+1} \]