Internal problem ID [2257]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 25, page 112
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+3 y^{\prime } x +y=1-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=1-x,y(x), singsol=all)
\[ y = \frac {c_{2}}{x}-\frac {x}{4}+1+\frac {c_{1} \ln \left (x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 26
DSolve[x^2*y''[x]+3*x*y'[x]+y[x]==1-x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x}{4}+\frac {c_1}{x}+\frac {c_2 \log (x)}{x}+1 \]