Find the value of k so that the given differential equation is exact. (³ + kxy¹ − 2x) dx +(3xy² +20x²y³) dy=0. Then find the implicit solution. Ⓒ10; xy³ +5x²y4 - x² = C O-10x²y³ + x² + x² = C -8; xy³-5x²y+ x = Ci ixy²-3xy + x² = C

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find the value of k so that the given differential equation is exact. (³+kxy-2x) dx +(3xy²+20x²y³) dy = 0. Then find
the implicit solution.
10; xy³ +5x²y4_x²=C
-10;
10₁x²y³ + x²y² + x² = C
-8; xy³-5x²y + x = Ci
xy²-3xy + x² = C
Transcribed Image Text:Find the value of k so that the given differential equation is exact. (³+kxy-2x) dx +(3xy²+20x²y³) dy = 0. Then find the implicit solution. 10; xy³ +5x²y4_x²=C -10; 10₁x²y³ + x²y² + x² = C -8; xy³-5x²y + x = Ci xy²-3xy + x² = C
Determine whether the DE is exact then find the implicit solution.
3y(x²-1)dx + (x³ + 8y-3x)dy=0; x = 0, y = 1
Ⓒx³y-3xy+4y² = 4
Ox³y-3xy+ 4y2²= -4
Ox³y-3xy-4y²=4
O x³y + 3xy+4y²=-4
Transcribed Image Text:Determine whether the DE is exact then find the implicit solution. 3y(x²-1)dx + (x³ + 8y-3x)dy=0; x = 0, y = 1 Ⓒx³y-3xy+4y² = 4 Ox³y-3xy+ 4y2²= -4 Ox³y-3xy-4y²=4 O x³y + 3xy+4y²=-4
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