Enter a problem... Calculus Examples Popular Problems Calculus Solve the Differential Equation x(yd)x+(x+1)dy=0 Step 1Subtract from both sides of the
equation.Step 2
Multiply both sides by .Step 3Simplify.
Tap for more steps...Step 3.1Cancel the
common factor of .
Tap for more steps...Step 3.1.1
Factor out of .Step 3.1.2Cancel the
common factor.Step 3.1.3Rewrite the
expression.Step 3.2Rewrite using the
commutative property of multiplication.Step 3.3Cancel the
common factor of .
Tap for more steps...Step 3.3.1Move the leading negative in into the
numerator.Step 3.3.2
Factor out of .Step 3.3.3
Factor out of .Step 3.3.4Cancel the
common factor.Step 3.3.5Rewrite the
expression.Step 3.4
Combine and .Step 3.5Move the negative in front of the
fraction.Step 4Integrate both sides.
Tap for more steps...Step 4.1
Set up an
integral on each side.Step 4.2The
integral of with respect to is .Step 4.3Integrate the right side.
Tap for more steps...Step 4.3.1Since is
constant with respect to , move out of the
integral.Step 4.3.2
Divide by .
Tap for more steps...Step 4.3.2.1
Set up the
polynomials to be divided. If there is not a
term for every
exponent, insert one with a value of .
Step 4.3.2.2
Divide the highest order
term in the
dividend by the highest order
term in
divisor .
Step 4.3.2.3
Multiply the new
quotient term by the
divisor.
Step 4.3.2.4The
expression needs to be subtracted from the
dividend, so change all the signs in
Step 4.3.2.5After changing the signs, add the last
dividend from the multiplied
polynomial to find the new
dividend.
Step 4.3.2.6The final answer is the
quotient plus the
remainder over the
divisor.Step 4.3.3Split the single
integral into
multiple integrals.Step 4.3.4Apply the
constant rule.Step 4.3.5Since is
constant with respect to , move out of the
integral.Step 4.3.6Let . Then . Rewrite using and .
Tap for more steps...Step 4.3.6.1Let . Find .
Tap for more steps...Step 4.3.6.1.1Differentiate .Step 4.3.6.1.2By the
Sum Rule, the
derivative of with respect to is .Step 4.3.6.1.3Differentiate using the
Power Rule which states that is where .Step 4.3.6.1.4Since is
constant with respect to , the
derivative of with respect to is .Step 4.3.6.1.5Add and .Step 4.3.6.2Rewrite the problem using and .Step 4.3.7The
integral of with respect to is .Step 4.3.8Simplify.Step 4.3.9Replace all occurrences of with .Step 4.3.10Simplify.
Tap for more steps...Step 4.3.10.1Apply the
distributive property.Step 4.3.10.2
Multiply .
Tap for more steps...Step 4.3.10.2.1
Multiply by .Step 4.3.10.2.2
Multiply by .Step 4.4Group the
constant of integration on the right side as .Step 5Solve for .
Tap for more steps...Step 5.1Move all the
terms containing a logarithm to the left side of the
equation.Step 5.2Use the
quotient property of logarithms, .Step 5.3To solve for , rewrite the
equation using
properties of logarithms.Step 5.4Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is
equivalent to .Step 5.5Solve for .
Tap for more steps...Step 5.5.1Rewrite the
equation as .Step 5.5.2
Multiply both sides by .Step 5.5.3Simplify the left side.
Tap for more steps...Step 5.5.3.1Cancel the
common factor of .
Tap for more steps...Step 5.5.3.1.1Cancel the
common factor.Step 5.5.3.1.2Rewrite the
expression.Step 5.5.4Solve for .
Tap for more steps...Step 5.5.4.1Reorder
factors in .Step 5.5.4.2Remove the
absolute value term. This creates a on the right side of the
equation because .Step 6Group the
constant terms together.
Tap for more steps...Step 6.1Rewrite as .Step 6.2Reorder and .Step 6.3
Combine constants with the
plus or
minus.
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