Multiply the original DE by xy:
xy2(1+x2y4+1−−−−−−−√)dx+2x2ydy=0(1)
Let v=xy2, so that dv=y2dx+2xydy. Then (1) becomes
x(y2dx+2xydy)+xy2x2y4+1−−−−−−−√dxxdv+vv2+1−−−−−√dx=0=0
This final equation is easily recognized as separable:
dxxln|x|+CKxvKx2y2−1K2x4y4−2Kx2y2y2=−dvvv2+1−−−−−√=ln∣∣∣v2+1−−−−−√+1v∣∣∣=v2+1−−−−−√+1=x2y4+1−−−−−−−√=x2y4=2KK2x2−1integrate both sides
<span>x=<span><span>1/2 </span>+ <span><span><span><span><span>−1/</span>6 </span><span>√33</span></span><span> or </span></span>x</span></span></span>=<span><span>1/2</span>+<span><span>1/6</span><span>√<span>33</span></span></span></span>
Answer:
0.1575 the fraction is 63/400, just divide 63 by 400
-by-step explanation:
Let's solve your equation step-by-step.
<span><span><span>−<span>x^2</span></span>−<span>2x</span></span>=5
</span>Step 1: Subtract 5 from both sides.
<span><span><span><span>−<span>x^2</span></span>−<span>2x</span></span>−5</span>=<span>5−5
</span></span><span><span><span><span>−<span>x^2</span></span>−<span>2x</span></span>−5</span>=0
</span>Step 2: Use quadratic formula with a=-1, b=-2, c=-5.
<span><span><span><span>
</span></span></span></span><span>x=(<span><span>2±<span>√<span>−16)/</span></span></span><span>−<span>2</span></span></span></span>