67.2.7 problem Problem 1(g)

Internal problem ID [13964]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 1(g)
Date solved : Tuesday, January 28, 2025 at 06:09:52 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 36

dsolve(cos(x)*diff(y(x),x)+y(x)*exp(x^2)=sinh(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.161 (sec). Leaf size: 66

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

\[ y(x)\to \exp \left (\int _1^x-e^{K[1]^2} \sec (K[1])dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}-e^{K[1]^2} \sec (K[1])dK[1]\right ) \sec (K[2]) \sinh (K[2])dK[2]+c_1\right ) \]