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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[@samueljoseph7220]

Fantastic of solving the simultaneous equations without any complex.😊

[@justadudewithsunglasses6798]

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.
You just earned a subscriber

[@ShivaniYadav-zj6xl]

Thankyou so much ,it is very helpful ❤

[@tahomidtonoy7479]

thank you

[@OpPhilo03]

Thank you very much mam❤❤

[@adithya4483]

Very good❤❤❤

[@user-xl1ig1bn6i]

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.

[@SwatiThengMathematics]

Thanks for the detailed explanation! Your method of subtracting equations to eliminate x and solving the resulting second-order non-homogeneous equation is clever. I appreciate your guidance and will consider implementing this approach in the future. Your expertise is valued!

[@Definitelynotdepressed]

Tysm!!

[@SwatiThengMathematics]

I'm glad you liked it. Feel free to share it with others too!😊

[@yoezernamgay2764]

Thank you madam welled explained 😃

[@mohitpardhi92]

Thank you madam

[@dhananjay1110]

Thanks for sem exam

[@kanchankumari7641]

Well explained 😀

[@sujalbandodkar1862]

Niceeee

[@SwatiThengMathematics]

Thank you

[@albiaclifordjanernib.5072]

What is your book source?

[@SwatiThengMathematics]

Engineering mathematics H K Dass and B S Grewal

[@ttsky1425]

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

[@SwatiThengMathematics]

Yes offline in Nagpur

[@ttsky1425]

@@SwatiThengMathematics I am from bhandara,
mam pass sa he hu.
Bsc ke 4 sem ke batch start hue hai kya?

[@SwatiThengMathematics]

@@ttsky1425 Yes

[@mohitpardhi92]

Mam I'm in nagpur

[@akashashwin4767]

Can u send the notes sis???

[@YansMar]

Very helpful, thanks!!

[@SwatiThengMathematics]

Thank you for your kind words! I'm delighted to hear that you found the video helpful. If you think it can benefit others, please consider sharing it with them. Your support means a lot!😊

[@roelequeen7194]

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