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The solution to the equation are as follows.
y = c₁ + c₂
What is differential equation?
In arithmetic, a equation is associate equation that relates one or a lot of unknown functions and their derivatives.
Main body:
Find the first derivative.
dy/dx=r
Find the second derivative.
d²y/dx² =r²
Substitute into the differential equation.
r²+4
=cos ²x
Factor out of r²
.
r²+4
=cos²x
Factor out of 4
.
r²+
⋅4=cos²x
Factor out of r²+4
(r²+4)=cos²x
Since exponentials can never be zero, divide both sides by
r²+4=cos²x
Use the double-angle identity to transform
cos²x to 1−sin²(x).
r² +4=1−sin²(x)
Subtract 4 from both sides of the equation.
r²=1−sin²(x)−4
Simplify the right side.
r² = -3 -sin²x
r = √-3 -sin²x
By the principle of superposition, the general solution is a linear combination of the two solutions for a second order homogeneous linear differential equation.
y = c₁ + c₂
Hence the differential solution is as follows.
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