83.5.5 problem 5

Internal problem ID [19100]
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 (D) at page 16
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 12:56:08 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 15

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

\[ y(x)\to \log (x)+\frac {c_1}{\log (x)} \]