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Exercise

dydx=xex2−y\frac { d y } { d x } = x e ^ { x ^ { 2 } - y }

Step-by-step Solution

Learn how to solve problems step by step online. Solve the differential equation dy/dx=xe^(x^2-y). Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression \frac{1}{e^{-y}}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Solve the differential equation dy/dx=xe^(x^2-y)

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Final answer to the exercise

y=ln⁡(e(x2)+C12)y=\ln\left(\frac{e^{\left(x^2\right)}+C_1}{2}\right)

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  • Product of Binomials with Common Term
  • FOIL Method
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dydx =xex2−y
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