83.2.7 problem 7

Internal problem ID [19053]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (A) at page 8
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 12:49:27 PM
CAS classification : [_Bernoulli]

\begin{align*} x y^{\prime }+y&=y^{2} \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.137 (sec). Leaf size: 20

DSolve[x*D[y[x],x]+y[x]==y[x]^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{\log (x)+c_1 x+1} \\ y(x)\to 0 \\ \end{align*}