75.16.50 problem 523

Internal problem ID [17023]
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. Trial and error method. Exercises page 132
Problem number : 523
Date solved : Tuesday, January 28, 2025 at 09:45:46 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} 7 y^{\prime \prime }-y^{\prime }&=14 x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(7*diff(y(x),x$2)-diff(y(x),x)=14*x,y(x), singsol=all)
 

\[ y = 7 \,{\mathrm e}^{\frac {x}{7}} c_{1} -7 x^{2}-98 x +c_{2} \]

✓ Solution by Mathematica

Time used: 4.921 (sec). Leaf size: 47

DSolve[7*D[y[x],{x,2}]-D[y[x],x]==14*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{\frac {K[2]}{7}} \left (c_1+\int _1^{K[2]}2 e^{-\frac {K[1]}{7}} K[1]dK[1]\right )dK[2]+c_2 \]