How to solve Simultaneous differential Equations using laplace transform | easy steps and method

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Solve 𝑥^′′+3𝑥−2𝑦=0, 〖𝑥^′′+𝑦〗^′′−3𝑥+5𝑦=0
with 𝑥(0)=0, 𝑥^′ (0)=1, 𝑦(0)=0, 𝑦^′ (0)=1
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[samueljoseph]

Fantastic of solving the simultaneous equations without any complex.😊

[justadudewithsunglasses]

I just want to say a big thank you. You explained perfectly. I know at some point you couldn't find the words in English to express what you wanted to say but I still understood anyway. I have an exam tomorrow and you just saved me.
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[ShivaniYadav-zjxl]

Thankyou so much, it is very helpful ❤

[AliBarisa]

You could have subtracted eqn (1) from eqn (2) to eliminate x''. Call the resultant eqn (3). Then move the term in x to the right so that you get a second order non-, homogeneous equation involving y an y" onthe LHS while the non-homogeneous term in x stays on the RHS. This way, you can solve the resultant ODE very fast to obtain the general solution of y=yc+yp.

Next, find y" and substitute both y and y" into eqn (3). Solve for for x using simple algebra. In this case, y is a function of x ie y(x). If u want it solve anather ODE, you can substitute y and y" into both eqn 1and 2, then add the two, to get an ODE that has x and x" as the only unknowns. Solve, the second ODE that obtain x.

[ttsky]

Welled expllained mam nice 👍
Ap tution leta hokya mam online/ofline?

[roelequeen]

Pliz use English throughout, i lost u when u started speaking another language