38.1.9 problem 9

Internal problem ID [6426]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Test excercise 24. page 1067
Problem number : 9
Date solved : Monday, January 27, 2025 at 02:02:36 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y \tanh \left (x \right )&=2 \sinh \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(diff(y(x),x)+y(x)*tanh(x)=2*sinh(x),y(x), singsol=all)
 

\[ y = \left (\cosh \left (x \right )^{2}-\frac {1}{2}+c_1 \right ) \operatorname {sech}\left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.093 (sec). Leaf size: 20

DSolve[D[y[x],x]+y[x]*Tanh[x]==2*Sinh[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \text {sech}(x) (\cosh (2 x)+2 c_1) \]