Show that any separable equation $M(x,y)+N(x,y){y}^{\prime}=0$

Tahmid Knox
2021-10-23
Answered

Show that any separable equation $M(x,y)+N(x,y){y}^{\prime}=0$

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mhalmantus

Answered 2021-10-24
Author has **106** answers

Differential equation with form $M(x,y)+N(x,y){y}^{\prime}=0$ is exact if:

${M}_{y}(x,y)={N}_{x}(x,y)$

In this case M is a function of x onle and therefore

${M}_{y}=0$

Also in this case N is a function of y only and therefore

${N}_{x}=0$

We see that${M}_{y}={N}_{x}=0$ so given equation is exact

In this case M is a function of x onle and therefore

Also in this case N is a function of y only and therefore

We see that

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