Q.14 solve x.e^x^2.e^ydx=y.dy@Educationalinfo786

### Description
This problem involves solving the differential equation \( x e^{x^2} e^y \, dx = y \, dy \). The goal is to find a relationship between the variables \( x \) and \( y \) through integration and algebraic manipulation. This is a part of the exercises from the Mathematical Methods course for BS/BSc, focusing on techniques to solve such differential equations.
Solve: e^x(1+dy/dx) = xe^-y | Exponential Differential Equation

### Hashtags
#DifferentialEquations
#Integration
#MathematicalMethods
#BScMath
#BSMath
#Exercise9_2
#Mathematics
#SolveDE
#Calculus
#IntegrationTechniques
#MathProblems
#UniversityMath
#AdvancedMath

### Keywords
- Differential equation,
- Integration,
- Mathematical Methods,
- BS Mathematics,
- BSc Mathematics,
- Exercise 9.2,
- Question 14,
- \( x e^{x^2} e^y \, dx = y \, dy \),
- Calculus,
- Integration techniques,
- Solve DE,
- University level math,
- Math problem solving,
- Advanced calculus,
solve: d^2y/dx^2-2dy/dx+y=x^2.e^2x,
solve the differential equation ye^x/ydx=(xe^x/y+y)dy,
solve: `(1+2e^(x/y))dx+2e^(x/y)(1-x/y)dy=0`,
solve the differential equation ye^(x/y)dx=(xe^(x/y)+y^2)dy,
solve this non exact differential equation,
how to solve double integrals,
solve the differential equation,
solve (1+e^x/y)dx+e^x/y(1-x/y)dy=0 | exercise-9.5 question-10 | ch-9,
ye^x/ydx=(xe^x/y+y^2)dy,
solution of xe^x²+y = ydy,