75.18.15 problem 604

Internal problem ID [17103]
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 15.3 Nonhomogeneous linear equations with constant coefficients. Initial value problem. Exercises page 140
Problem number : 604
Date solved : Tuesday, January 28, 2025 at 09:52:48 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=-2 x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 18

dsolve([diff(y(x),x$3)-diff(y(x),x)=-2*x,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 2],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x}}{2}-\frac {{\mathrm e}^{-x}}{2}+x^{2} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 25

DSolve[{D[y[x],{x,3}]-D[y[x],x]==-2*x,{y[0]==0,Derivative[1][y][0] ==1,Derivative[2][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2-\frac {e^{-x}}{2}+\frac {e^x}{2} \]