75.14.21 problem 347

Internal problem ID [16935]
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 ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 347
Date solved : Tuesday, January 28, 2025 at 09:42:41 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }+2&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 7

dsolve([diff(y(x),x$2)+diff(y(x),x)+2=0,y(0) = 0, D(y)(0) = -2],y(x), singsol=all)
 

\[ y = -2 x \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 8

DSolve[{D[y[x],{x,2}]+D[y[x],x]+2==0,{y[0]==0,Derivative[1][y][0] ==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 x \]