Internal problem ID [15425]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 660.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+y^{\prime }={\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+diff(y(x),x)=exp(2*x)*cos(exp(x)),y(x), singsol=all)
\[ y \left (x \right ) = \left (-c_{1} +2 \sin \left ({\mathrm e}^{x}\right )\right ) {\mathrm e}^{-x}+c_{2} -\cos \left ({\mathrm e}^{x}\right )-1 \]
✓ Solution by Mathematica
Time used: 0.258 (sec). Leaf size: 32
DSolve[y''[x]+y'[x]==Exp[2*x]*Cos[Exp[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-e^{-x} \left (-2 \sin \left (e^x\right )+e^x \cos \left (e^x\right )+c_1\right ) \]