Answered

Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Verify by substitution that the given function is a solution of the given differential equation.x2y′′ + xy′ −y = ln x, y = x −ln x

Sagot :

LammettHash

Looks like the differential equation is

x² y'' + x y' - y = ln(x)

and the known solution is

y = x - ln(x)

Take the first derivatives of the solution:

y' = 1 - 1/x

y'' = 1/x²

Substitute y and its derivatives into the DE:

x² (1/x²) + x (1 - 1/x) - (x - ln(x)) = ln(x)

If y is a valid solution, then this equation should reduce to an identity.

1 + x - 1 - x + ln(x) = ln(x)

0 = 0   ✓

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.