(2xy^4e^y+2xy^3+y)dx+(x^2y^4e^y-x^2y^2-3x)dy=0 #NonExact L616 @MathsPulseChinnaiahKalpana

#nonexactequation #reducibletoexact Hello, People! Here is a video of solving non-exact equation, by reducing the given equation exact form. Have a little patience and watch the video till end. My hearty thanks to all the subscribers, supporters, viewers and well-wishers❤ With Love, Chinnaiah Kalpana🍁 Note: Ordinary Differential Equation(ODE): A differential equation is said to be ordinary, if the derivatives in the equation have reference to only a single independent variable. If (1/M)[(partial derivative of N w.r.t. x) - (partial derivative of M w.r.t. y)] = g(y) [i.e., a function of y only] (or) k [real number] , then exp(∫g(y)dy) (or) exp(∫kdy) is an integrating factor of Mdx+Ndy=0. exp(log g(y)) = g(y) & exp(k logy) = exp[log(y^k)] = y^k where k is constant. Working rule to solve Mdx+Ndy=0: 1. General equation is Mdx+Ndy=0 ......(i) Observe (partial derivative of M w.r.t. y) ≠ (partial derivative of N w.r.t. x), then (i) is Non-Exact. 2. Find (1/M)[(partial derivative of N w.r.t x) - (partial derivative of M w.r.t y)] and observe it as a function of y alone = g(y) or a real constant k. 3. Then exp(∫g(y)dy) or exp(∫kdy) is an Integrating factor of (i). 4. Multiplying (i) with I.F. to transform it into an exact equation of (i), M1dx+N1dy=0 ...(ii) 5. Solve (ii) to get the general solution of (i). For more such videos 👇    • Differential Equations- Engineering Mathem...   I'm on Instagram👇   / mathspulse_chinnaiahkalpana   Stay tuned to 'Maths Pulse'. Get rid of 'Maths Phobia'. Have a happy learning! #differentialequations #mathspulse #chinnaiahkalpana #nonexactproblems #engineeringmathematics #bscmaths #maths #math