1.29 problem 29

Internal problem ID [7993]
Book : First order enumerated odes
Section : section 1
Problem number : 29
Date solved : Friday, October 25, 2024 at 12:53:23 PM
CAS classification : [_Riccati]

Solve

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

Unknown ode type.

1.29.1 Maple step by step solution

\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & y^{\prime }=\cos \left (x \right )+\frac {y^{2}}{x} \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & y^{\prime } \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & y^{\prime }=\cos \left (x \right )+\frac {y^{2}}{x} \end {array} \]

1.29.2 Maple trace

Methods for first order ODEs:
 

1.29.3 Maple dsolve solution

Solving time : 0.322 (sec)
Leaf size : maple_leaf_size

dsolve(diff(y(x),x) = cos(x)+y(x)^2/x, 
       y(x),singsol=all)
 

\[ \text {No solution found} \]

1.29.4 Mathematica DSolve solution

Solving time : 0.0 (sec)
Leaf size : 0

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

Not solved