69.1.111 problem 158

Internal problem ID [14264]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 158
Date solved : Tuesday, January 28, 2025 at 06:24:55 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=2 x +3 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)+5*diff(y(x),x)-2*y(x)=2*x+3,y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} c_{2} +\left (c_{3} x +c_{1} \right ) {\mathrm e}^{x}-x -4 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 31

DSolve[D[y[x],{x,3}]-4*D[y[x],{x,2}]+5*D[y[x],x]-2*y[x]==2*x+3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^x+x \left (-1+c_2 e^x\right )+c_3 e^{2 x}-4 \]