Internal problem ID [10880]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\cos \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}}-\sinh \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(cos(x)*diff(y(x),x)+y(x)*exp(x^2)=sinh(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\int {\mathrm e}^{\int {\mathrm e}^{x^{2}} \sec \left (x \right )d x} \sinh \left (x \right ) \sec \left (x \right )d x +c_{1} \right ) {\mathrm e}^{\int -{\mathrm e}^{x^{2}} \sec \left (x \right )d x} \]
✓ Solution by Mathematica
Time used: 0.975 (sec). Leaf size: 66
DSolve[Cos[x]*y'[x]+y[x]*Exp[x^2]==Sinh[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}