35.6.22 problem 22

Internal problem ID [6172]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 22
Date solved : Monday, January 27, 2025 at 01:46:27 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(2*diff(y(x),x$2)+diff(y(x),x)=2*x,y(x), singsol=all)
 

\[ y = -2 \,{\mathrm e}^{-\frac {x}{2}} c_1 +x^{2}-4 x +c_2 \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 23

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

\[ y(x)\to x^2-2 x-c_1 e^{-x}+c_2 \]