77.1.132 problem 159 (page 236)

Internal problem ID [18022]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 159 (page 236)
Date solved : Tuesday, January 28, 2025 at 11:20:41 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=\frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-y(x)=( exp(x)-exp(-x))/(exp(x)+exp(-x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.417 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]-y[x]==(Exp[x]-Exp[-x])/(Exp[x]+Exp[-x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\left (e^{2 x}+1\right ) \arctan \left (e^x\right )+c_1 e^{2 x}+c_2\right ) \]