Write the first order differential equation for y=2-int_0^x(1+y(t))sin tdt

Lewis Harvey 2020-10-23 Answered

Write the first order differential equation for y=20x(1+y(t))sintdt

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Expert Answer

brawnyN
Answered 2020-10-24 Author has 91 answers

Now differentiating this with respect to x
dy/dx=d/dx[20x(1+y(t))sintdt]
dy/dx=d/dx[2]d/dx[0x(1+y(t))sintdt]
dy/dx=0[(1+y(t))sin(x)d/dx(x)(1+y(0))sin(0)d/dx(0)]
dy/dx=[(1+y(x))sinx(1)(1+y(0))(0)0]
dy/dx=[(1+y(x))sinx0]
dy/dx=(1+y(x))sinx
y=(1+y)sinx

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