We are given that  dy/dt = 5y - 6t

rearranging which, we get, dy = 5y.dt - 6t.dt

Integrating both sides, we get

y = 5y.t - 3(t^2) + c

Given, y(0) = -2

which gives,

-2 = 0 + 0 +c

implies C = -2

Hence, the required equation is y = 5y.t - 3(t^2) - 2.

Hope it helps.

Hello Aspirant,

I'll recommend you to go through previous year paper for important questions and answers. Also you can purchase few books for sample question papers. These books covers almost all the important area of the subject. Solving these will help you with better understanding and practice.

Good Luck

Hello Prathik,

Hope everything going well.

Here is a method from which you can solve such equation:

Multiplying by 2x/x^2

2(xdx+ydy)+4y(xdy−ydx)/x^2=0

d(x^2+y^2)+4yd(y/x)=0

Converting to polar co ordinates

d(r^2)+4rsinθd(tanθ)=0

2rdr+4rsinθsec^2(θ)dθ=0

2rdr+4rsinθsec^2(θ)dθ=0

dr+2secθtanθdθ=0

Integrating,

r+2secθ=C

√( x^2+y^2)+2 √( 1+tan^2(θ))=C

√( x^2+y^2)+2 √( 1+(y^2/x^2))=C

(x+2) √(x^2+y^2)=Cx

Hope this helps you. Thank you.

All the best!!

Hi there!

Greetings!

Hope you are having a nice day!

Here I am giving you that notes of ordinary differential equation of IIT kharagpur :- http://www.math.iitb.ac.in/~siva/afs07.pdf so you can use it any I hope it might help you alot. So keep learning keep practicing and keep growing.

All the best for your future!

Thanks.

Hello Nirmal,

(2x+4y-6)dy=(2x-5y +3)dx

This is a very common type of  question that usually comes in the exams . This question is probably from the chapter of Differential Equations. As you understand that it is not that easy to solve the entire question here in the chat box so I have found an online solution of the equation that would help you.

Here's the link that will take you to the solution :-

https://math.stackexchange.com/questions/2001575/2x-5y3dx-2x4y-6dy/2001597#2001597

I hope it helped.

All the best.

Hey there

Maths and chemistry are scoring. Chemistry has no long writing SA type questions and thus you can score maximum in this subject. Physics has derivations and thus you have to learn stepwise skill to write derivations. Maths is calculative but write neat and clean do not cross too much in the question. Point wise writing is important.

Good luck