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Masteriza [31]
3 years ago
10

Obtain the general solution to the equation. (x^2+10) + xy = 4x=0 The general solution is y(x) = ignoring lost solutions, if any

.
Mathematics
1 answer:
alukav5142 [94]3 years ago
6 0

Answer:

y(x)=4+\frac{C}{\sqrt{x^2+10}}

Step-by-step explanation:

We are given that a differential equation

(x^2+10)y'+xy-4x=0

We have to find the general solution of given differential equation

y'+\frac{x}{x^2+10}y-\frac{4x}{x^2+10}=0

y'+\frac{x}{x^2+10}y=4\frac{x}{x^2+10}

Compare with

y'+P(x) y=Q(x)

We get

P(x)=\frac{x}{x^2+10}

Q(x)=\frac{4x}{x^2+10}

I.F=e^{\int\frac{x}{x^2+10} dx}=e^{\frac{1}{2}ln(x^2+10)}

e^{ln\sqrt(x^2+10)}=\sqrt{x^2+10}

y\cdot \sqrt{x^2+10}=\int \frac{4x}{x^2+10}\times \sqrt{x^2+10} dx+C

y\cdot \sqrt{x^2+10}=\int \frac{4x}{\sqrt{x^2+10}}+C

y\cdot \sqrt{x^2+10}=4\sqrt{x^2+10}+C

y(x)=4+\frac{C}{\sqrt{x^2+10}}

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