# Two-variable linear equations Calculator

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### Difficult Problems

1

Example

$y''+4y=\cos\left(x\right)$
2

Subtract $y''$ from both sides of the equation

$4y=y''\left(-1\right)+\cos\left(x\right)$
3

Multiply both sides of the equation by 

$y=\frac{1}{4}\left(y''\left(-1\right)+\cos\left(x\right)\right)$
4

Applying the cosine identity: $\displaystyle\cos\left(\theta\right)=\frac{1}{\sec\left(\theta\right)}$

$y=\frac{1}{4}\left(y''\left(-1\right)+\frac{1}{\sec\left(x\right)}\right)$
5

Applying the trigonometric identity: $\displaystyle\frac{1}{\sec(\theta)}=\cos(\theta)$

$y=\frac{1}{4}\left(y''\left(-1\right)+\cos\left(x\right)\right)$