83.30.12 problem 12

Internal problem ID [19391]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 01:37:10 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

\[ y \left (x \right ) = \frac {x^{2}}{4}+\ln \left (x \right ) c_{1} +c_{2} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 20

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

\[ y(x)\to \frac {x^2}{4}+c_1 \log (x)+c_2 \]