Solving x^2 D2y - x Dy + y = log(x) - SOLUTION EXPLAINED

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Solve: x log x dy/dx+y=2 log x || First order ODE|| Integrating factor|| #ode #integrating_factor Solve: x log x dy/dx+y=2 log x || First order ODE|| Integrating factor|| #ode #integrating_factor
Let y(x) be the solution of the differential equation (xlogx) (dy)/(dx) +y=2x log x..Then y(e) Let y(x) be the solution of the differential equation (xlogx) (dy)/(dx) +y=2x log x..Then y(e)
#44 || Problem#4 || Cauchy’s linear equation|| Solve 𝒙^𝟐 (𝒅^𝟐 π’š)/〖𝒅𝒙〗^𝟐 βˆ’π’™ π’…π’š/𝒅𝒙+π’š=π’π’π’ˆπ’™ || #44 || Problem#4 || Cauchy’s linear equation|| Solve 𝒙^𝟐 (𝒅^𝟐 π’š)/〖𝒅𝒙〗^𝟐 βˆ’π’™ π’…π’š/𝒅𝒙+π’š=π’π’π’ˆπ’™ ||
(x^2D^2+xD+1)y=(logx)Sin(logx) #CauchyEulerLinearEquation L919 (x^2D^2+xD+1)y=(logx)Sin(logx) #CauchyEulerLinearEquation L919
Logarithmic Function Differentiation: How to Differentiate Logarithmic Functions #excellenceacademy Logarithmic Function Differentiation: How to Differentiate Logarithmic Functions #excellenceacademy
Solve: xy Solve: xy'+ y= y^2 log x|| Example of Bernoulli's equation || Step-by-step solution.
If x dy/ dx = y(log y – log x + 1), then the solution of the equation is If x dy/ dx = y(log y – log x + 1), then the solution of the equation is
'x log(x) dy/dx+y=2/x logx' || x log x dy/dx+y= 2/x log x' || xlogxdy/dx+y=2/xlogx ||