60.1.5 problem 5

Internal problem ID [10019]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 5
Date solved : Monday, January 27, 2025 at 06:18:26 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y \cos \left (x \right )-{\mathrm e}^{2 x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(diff(y(x),x) + y(x)*cos(x) - exp(2*x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 52

DSolve[D[y[x],x] + y[x]*Cos[x] - Exp[2*x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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