75.20.3 problem 638

Internal problem ID [17137]
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 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 638
Date solved : Tuesday, January 28, 2025 at 09:54:03 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (1+x \right ) y^{\prime }+6 y&=6 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 15

dsolve((3*x+2*x^2)*diff(y(x),x$2)-6*(1+x)*diff(y(x),x)+6*y(x)=6,y(x), singsol=all)
 

\[ y = c_{2} x^{3}+c_{1} x +c_{1} +1 \]

✓ Solution by Mathematica

Time used: 0.221 (sec). Leaf size: 164

DSolve[(3*x+2*x^2)*D[y[x],{x,2}]-6*(1+x)*D[y[x],x]+6*y[x]==6,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \exp \left (\int _1^x\frac {3 (K[1]+2)}{K[1] (2 K[1]+3)}dK[1]-\frac {1}{2} \int _1^x-\frac {6 (K[2]+1)}{K[2] (2 K[2]+3)}dK[2]\right )+c_2 \exp \left (\int _1^x\frac {3 (K[1]+2)}{K[1] (2 K[1]+3)}dK[1]-\frac {1}{2} \int _1^x-\frac {6 (K[2]+1)}{K[2] (2 K[2]+3)}dK[2]\right ) \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {3 (K[1]+2)}{K[1] (2 K[1]+3)}dK[1]\right )dK[3]+1 \]