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laplace transform ty^{\prime}+2y=t^2-t+1,y(1)= 1/2

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

laplace bernoulli substitution linear exact

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gram-schmidt (

), (

)

Solution

e₁=(

), e₂=(

), e₃=(

)

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Solution steps

One step at a time

v₁=(

), v₂=(

), v₃=(

)

Gram-Schmidt process

For a finite, linearly independent set of vectors v₁, … v_k, u_k=v_k−∑_j=1^k−1proj_{u_j}(v_k),
where proj_u(v)=v · u|u|² u.
The normalized vector is e_k=u_k|u_k|

Orthonormalize v₁=(

): (

)

Orthonormalize v₂=(

): (

)

Orthonormalize v₃=(

): (

)

e₁=(

), e₂=(

), e₃=(

)

Linear First Order Differential Equations Examples

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),(

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

laplace transform ty^{\prime}+2y=t^2-t+1,y(1)= 1/2

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Solution steps

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