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Solve the differential equation dy/dx=sin(x+y) Please answer this question

Solve the differential equation dy/dx=sin(x+y)
Please answer this question

Grade:12th pass

2 Answers

Khimraj
3007 Points
5 years ago
now assume tanv/2 = t and solve further.   This is the solution.\int \frac{sec^2\frac{v}{2}dv}{1+2tan\frac{v}{2}+tan^{2}\frac{v}{2}}= \int dx \int \frac{dv}{1+\frac{2tan\frac{v}{2}}{1+tan^2\frac{v}{2}}}= \int dx \int \frac{dv}{1+sinv}= \int dx Integrate both sides\frac{dv}{1+sinv}= dx Using variable and separable method\frac{dv}{dx}-1= sin(v) \frac{dy}{dx} = sin(x+y)Put x+y = v1+dy/dx = dv/dxdy/dx = dv/dx – 1
Khimraj
3007 Points
5 years ago
Put x+y = v
1+dy/dx = dv/dx
dy/dx = dv/dx – 1
 \frac{dy}{dx} = sin(x+y)
\frac{dv}{dx}-1= sin(v)
Using variable and separable method
\frac{dv}{1+sinv}= dx 
Integrate both sides
 \int \frac{dv}{1+sinv}= \int dx
\int \frac{dv}{1+\frac{2tan\frac{v}{2}}{1+tan^2\frac{v}{2}}}= \int dx 
\int \frac{sec^2\frac{v}{2}dv}{1+2tan\frac{v}{2}+tan^{2}\frac{v}{2}}= \int dx
now assume tanv/2 = t and solve further.   This is the solution.
 

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