find general solution to: x(dy/dx) + 2y = 4x^2

Divide through by x so:      (dy/dx) +2(y/x) = 4x

Now multiply through by the intergrating factor:  e^(| (2/x) dx) = e^(2.ln(x)) = x^2

so you get:     (x^2)(dy/dx) + 2xy = 4(x^3)

Now integrate the entire equation and you get:        y(x^2) = |(4(x^3))dx = (x^4) + c

Divide through by (x^2) to get the general solution:

y = (x^2) + 4/(x^2)

Matthew P. 11 Plus Maths tutor, GCSE Maths tutor, A Level Maths tutor...

8 months ago

Answered by Matthew, an A Level Further Mathematics tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£20 /hr

Izzy A.

Degree: Mathematics and Philosophy (Bachelors) - Durham University

Subjects offered:Further Mathematics , Maths

Further Mathematics

“I am a 19-year-old, currently in my 2nd year at Durham University studying Maths and Philosophy. ”

£36 /hr

Joe B.

Degree: Mathematics G100 (Bachelors) - Bath University

Subjects offered:Further Mathematics , Maths+ 4 more

Further Mathematics
-Personal Statements-

“About Me Hi, I'm Joe, a first year mathematics student from Luton studying at Bath University. I am an accomplished mathematician and economist, having achieved A* grades in A Level Maths, Further Maths and Economics in June 2016. As ...”

Alec S. A Level Maths tutor, GCSE Maths tutor, 13 Plus  Maths tutor, ...
£20 /hr

Alec S.

Degree: Mechanical Engineering (Masters) - Leeds University

Subjects offered:Further Mathematics , Maths+ 1 more

Further Mathematics

“2nd year mechanical engineering student at the University of Leeds. Passionate mathematician. Top 1st year mark in engineering faculty.”

About the author

Matthew P.

Currently unavailable: for new students

Degree: Electronic & Electrical Engineering (Bachelors) - Southampton University

Subjects offered:Further Mathematics , Physics+ 1 more

Further Mathematics

“About me: I'm an undergarduate Electronic Engineer studying at the University of Southampton. I really enjoy working on new projects, such as designing robots and other rasberry pi projects, and it stems from a love of Physics and Mat...”

MyTutor guarantee

You may also like...

Posts by Matthew

Convert the decimal number 165 to binary

Explain the difference between forced vibration and resonance in an oscillating object.

find general solution to: x(dy/dx) + 2y = 4x^2

Find Solution to x^2 + x - 2=0

Other A Level Further Mathematics questions

Integrate (x+4)/(x^2+2x+2)

Prove by induction that n^3+5n is divisible by 3 for every natural number.

Using mathematical induction, prove that n^3+2n is divisible by 3 for all integers n

What is a complex number?

View A Level Further Mathematics tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss